Sum of torques/friction problem

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To determine the coefficient of static friction for a 7.1 m aluminum ladder leaning against a frictionless wall, the problem requires applying the conditions for equilibrium, specifically the sum of forces and torques. The ladder slips at a 52° angle, indicating that static friction is at its maximum just before slipping occurs. A free body diagram is essential for visualizing the forces acting on the ladder, including the weight, normal force, and frictional force. Understanding that the frictional force must equal the normal force in the horizontal direction is crucial for solving the problem. The focus should remain on static friction, as the ladder is on the verge of slipping.
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Homework Statement



What is the magnitude of the horizontal
A uniform 7.1 m tall aluminum ladder is leaing against a frictionless vertical wall. The
ladder has a weight of 227 N. The ladder slips
when it makes a 52.0◦ angle with the horizontal floor.
Determine the coefficient of static friction
between the ladder and the floor

Homework Equations


sum of torquest ET=0 and Newtons second EF=ma



The Attempt at a Solution



We did a problem like this in class today but we didnt take the coefficient of friction into account I am not sure where to start with this... I have drawn a diagram... and since It slips at 52 degrees i believe that is kinetic friction... rather than the static friction coefficient which i am trying to find out. If i go thought the sum of torques equation i find out that the force force of friction in the x direction should equal the normal force as the ladder pushes against the wall... could some one please help me understand this concept a little better?
 
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ddn87 said:
and since It slips at 52 degrees i believe that is kinetic friction... rather than the static friction coefficient which i am trying to find out.
No, all you need to worry about is static friction. The ladder is at the point where it is just about to slip, so static friction is at its maximum.
If i go thought the sum of torques equation i find out that the force force of friction in the x direction should equal the normal force as the ladder pushes against the wall... could some one please help me understand this concept a little better?
Apply all the conditions for equilibrium: ΣF = 0 and ΣT = 0.

Draw a free body diagram of the ladder.
 

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